Miscounts, Duverger's Law and Duverger's Hypothesis
IGIER Working Paper No. 380
37 Pages Posted: 9 Apr 2011
Date Written: January 5, 2011
In real-life elections, vote-counting is often imperfect. We analyze the consequences of such imperfections in plurality and runoff rule voting games. We call a strategy profile a robust equilibrium if it is an equilibrium if the probability of a miscount is positive but small.
All robust equilibria of plurality voting games satisfy Duverger's Law: In any robust equilibrium, exactly two candidates receive a positive number of votes. Moreover, robustness (only) rules out a victory of the Condorcet loser.
All robust equilibria under runoff rule satisfy Duverger's Hypothesis: First round votes are (almost always) dispersed over more than two alternatives. Robustness has strong implications for equilibrium outcomes under runoff rule: For large parts of the parameter space, the robust equilibrium outcome is unique.
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